Real analytic Eisenstein series information

simplest real analytic Eisenstein series is a special function of two variables. It is used in the representation theory of SL(2,R) and in analytic number...

Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written...

Eisenstein's theorem Eisenstein triple Eisenstein–Kronecker number Real analytic Eisenstein series Elliptic Gauss sum "Eisenstein biography". Archived...

Kronecker limit formula describes the constant term at s = 1 of a real analytic Eisenstein series (or Epstein zeta function) in terms of the Dedekind eta function...

functional equations. Harmonic Maass form Mock modular form Real analytic Eisenstein series Automorphic form Modular form Voronoi formula Bringmann, Kathrin;...

coefficients of representations of Lie groups. Theta functions and real analytic Eisenstein series, important in algebraic geometry and number theory, also admit...

evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes...

field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions...

sense as a Puiseux series—because the exponents have unbounded denominators—the original equation has no solution. However, such Eisenstein equations are essentially...

1007/BF02139701 with Dorian Goldfeld: Eisenstein series of half integral weight and the mean value of real Dirichlet L-series, Inv. Math., vol. 80, 1985, pp...

number theory. His contributions include works on p-adic L functions and real-analytic automorphic forms. His work on p-adic L-functions, later recognised...

perform this analytic continuation will lead to the same result, by the identity theorem. A first step in this continuation observes that the series for the...

using complex numbers Analytic continuation Complex-base system Complex geometry Geometry of numbers Dual-complex number Eisenstein integer Geometric algebra...

"discrete spectrum", contrasted with the "continuous spectrum" from Eisenstein series. It becomes much more technical for bigger Lie groups, because the...

of Fermat's last theorem and created analytic number theory. In analysis, he advanced the theory of Fourier series and was one of the first to give the...

or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, for example...

MR 2605321 Zwegers, S. P. (2001), "Mock θ-functions and real analytic modular forms", q-series with applications to combinatorics, number theory, and physics...

In mathematics, a modular form is a (complex) analytic function on the upper half-plane, H {\displaystyle \,{\mathcal {H}}\,} , that satisfies: a kind...

Society. Second Series. 26 (3): 198–204. doi:10.1112/jlms/s1-26.3.198. MR 0041889. Cox, David A. (2011). "Why Eisenstein proved the Eisenstein criterion and...

is harder, because there is a continuous spectrum, described using Eisenstein series. Selberg worked out the non-compact case when G is the group SL(2...

are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice. It has an aspect belonging to the theory of special functions...

identities, including relationships on the Riemann zeta function and the Eisenstein series of modular forms. Divisor functions were studied by Ramanujan, who...

)=-{\frac {B_{k,\chi }}{k}},} where L(s,χ) is the Dirichlet L-function of χ. Eisenstein–Kronecker numbers are an analogue of the generalized Bernoulli numbers...